Multiple time series of environmental quality data with similar, but not necessarily identical, trends call for multivariate methods for trend detection and adjustment for covariates. Here, we show how an additive model in which the multivariate trend function is specified in a nonparametric fashion (and the adjustment for covariates is based on a parametric expression) can be used to estimate how the human impact on an ecosystem varies with time and across components of the observed vector time series. More specifically, we demonstrate how a roughness penalty approach can be utilized to impose different types of smoothness on the function surface that describes trends in environmental quality as a function of time and vector component. Compared to other tools used for this purpose, such as Gaussian smoothers and thin plate splines, an advantage of our approach is that the smoothing pattern can easily be tailored to different types of relationships between the vector components. We give explicit roughness penalty expressions for data collected over several seasons or representing several classes on a linear or circular scale. In addition, we define a general separable smoothing method. A new resampling technique that preserves statistical dependencies over time and across vector components enables realistic calculations of confidence and prediction intervals.

The demands on monitoring systems have gradually increased, and interpretation of the data is often a matter of controversy. As an example of this, we investigated water quality monitoring and the eutrophication issue in Sweden. Our results demonstrate that powerful statistical tools for trend analysis can reveal flaws in the data and lead to new and revised interpretations of environmental data. In particular, we found strong evidence that long-term trends in measured nutrient concentrations can be more extensively influenced by changes in sampling and laboratory practices than by actual changes in the state of the environment. On a more general level, our findings raise important questions regarding the need for new paradigms for environmental monitoring and assessment. Introduction of a system in which conventional quality assurance is complemented with thorough statistical follow-up of reported values would represent a first step towards recognizing that environmental monitoring and assessment should be transformed from being a system for sampling and laboratory analyses into a system for interpreting information to support policy development.

Assessing regional trends in groundwater quality can be a difficult task. Data are often scattered in space and time, and the inertia of groundwater systems can create natural, seemingly persistent changes in concentration that are difficult to separate from anthropogenic trends. Here, we show how statistical methods and software for joint analysis of multiple time series can be integrated into a roadmap for trend analysis and critical examination of data quality. Ordinary and partial Mann-Kendall (MK) tests for monotonic trends and semiparametric smoothers for multiple time series constitute the cornerstones of our procedure. The MK tests include a simple and easily implemented method to correct for serial dependence, and the associated software is designed to enable convenient handling of numerous data series and to accommodate covariates and nondetects. The semiparametric smoothers are intended to facilitate detection of synchronous changes in a network of stations. A study of Swedish groundwater quality data revealed true upward trends in acid-neutralizing capacity (ANC) and downward trends in sulphate, but also a misleading shift in alkalinity level that would have been difficult to detect if the time series had been analysed separately.

Changes in observational data over time can be severely distorted by errors in measurements, sampling, or reporting. Here, we show how smooth trends in vector time series can be separated from one or two abrupt level shifts that occur simultaneously in all coordinates. Trends are modelled nonparametrically, whereas abrupt changes and the impact of covariates are modelled parametrically. The model is estimated using a backfitting algorithm in which estimation of smooth trends is alternated with estimation of regression coefficients for covariates and assessment of sudden level shifts. The proposed method is adaptive in the sense that the degree of smoothing over time and across coordinates is controlled by a roughness penalty and cross-validation procedure that automatically identifies the interdependence of the analysed data. Furthermore, it uses a resampling technique that can accommodate correlated error terms in the assessment of the uncertainty of both smooth trends and discontinuities. The method is applied to water quality data from Swedish national monitoring programmes to illustrate how known discontinuities can be quantified and how previously unrecognized discontinuities can be detected.

Process-oriented models of the retention of nitrogen in catchments are by necessity rather complex. We introduced several types of ensemble runs that can provide informative summaries of meteorologically normalised model outputs and also clarify the extent to which such outputs are related to various model parameters. Thereafter we employed this technique to examine policy-relevant outputs of the catchment model INCA-N. In particular, we examined how long it will take for changes in the application of fertilisers on cultivated land to affect the predicted riverine loads of nitrogen. The results showed that the magnitude of the total intervention effect was influenced mainly by the parameters governing the turnover of nitrogen in soil, whereas the temporal distribution of the water quality response was determined primarily by the hydromechanical model parameters. This raises the question of whether the soil nitrogen processes included in the model are elaborate enough to correctly explain the widespread observations of slow water quality responses to changes in agricultural practices.